I can remember when mostly only students in private schools had a 'year out' gap year and took the Oxbridge exams after tutoring in their 'seventh term' at sixth form giving them an advantage over state school pupils. I wonder if that will still be allowed?
But the current tests are very different from the exams of the 80s and before. The current tests do not directly exam the material taught at A level, but look for higher level understanding and thinking. So tutoring for the tests has significantly less effect than it would have done in the old days.
Some students do apply to Oxbridge after finishing A levels, particularly when they did better than expected. But they are not at an advantage, as they are expected to be at a higher level than applicants from year 13.
There is a concern that any form of pre-tests is a barrier for kids from disadvantaged backgrounds and I personally am not really in favour of pre-tests. But the results of the pre-tests are certainly looked at in context, so students from top private schools would be expected to perform quite a bit better than those from disadvantaged backgrounds to get through to interview stage.